Finite Group Databasebeta

← C137×#25822 #46875208

Subgroups — C137×#25822 #46875208

Order 35072.

982 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C137C211yesmaximal, characteristic
2C2×#501×C137C211yesmaximal, characteristic, complemented
3C2×#499×C137C211yesmaximal, characteristic, complemented
4#2629×C137C211yesmaximal, characteristic
5#2059×C137C211yesmaximal, characteristic, complemented
6#2059×C137C211yesmaximal, characteristic, complemented
7#2058×C137C211yesmaximal, characteristic, complemented
8#2057×C137C211yesmaximal, characteristic, complemented
9#1992×C137C211yesmaximal, characteristic, complemented
10#1990×C137C211yesmaximal, characteristic, complemented
11#1854×C137C211yesmaximal, characteristic
12#1854×C137C211yesmaximal, characteristic
13#1853×C137C211yesmaximal, characteristic
14#1852×C137C211yesmaximal, characteristic
15#1750×C137C211yesmaximal, characteristic
16#544×C137—24no—
17#544×C137—24no—
18C2×C4⋊Q8×C137—21no—
19C2×C4⋊Q8×C137C2211yescharacteristic
20C2×C4⋊Q8×C137C2211yescharacteristic
21C2×#125×C137—21no—
22C2×#125×C137C2211yescharacteristic
23C2×#125×C137C2211yescharacteristic
24C2×#125×C137C2211yescharacteristic
25C2×C22⋊Q8×C137—21no—
26C2×C22⋊Q8×C137—21no—
27C2×#117×C137C2211yescharacteristic
28C2×#117×C137C2211yescharacteristic
29C22×C4⋊C4×C137C2211yescharacteristic
30#501×C137—24no—
31#499×C137—24no—
32C2×#107×C137C2211yescharacteristic
33C2×#107×C137C2211yescharacteristic
34C2×#107×C137C2211yescharacteristic
35C2×#107×C137C2211yescharacteristic
36C2×#106×C137C2211yescharacteristic
37C2×#106×C137C2211yescharacteristic
38C2×#106×C137C2211yescharacteristic
39C2×#106×C137C2211yescharacteristic
40C2×C22⋊C8×C137C2211yescharacteristic
41C2×C22⋊C8×C137C2211yescharacteristic
42C2×#97×C137C2211yescharacteristic
43C2×C4×C8×C137C2211yescharacteristic
44#398×C137—21no—
45#398×C137—21no—
46#396×C137—21no—
47#396×C137—21no—
48#389×C137C2211yescharacteristic
49#389×C137C2211yescharacteristic
50#384×C137C2211yescharacteristic
51#380×C137C2211yescharacteristic
52#380×C137C2211yescharacteristic
53#340×C137C2211yescharacteristic
54#340×C137C2211yescharacteristic
55#340×C137C2211yescharacteristic
56#340×C137C2211yescharacteristic
57#340×C137C2211yescharacteristic
58#340×C137C2211yescharacteristic
59#340×C137C2211yescharacteristic
60#340×C137C2211yescharacteristic
61#336×C137C2211yescharacteristic
62#336×C137C2211yescharacteristic
63C22×Q8×C137—21no—
64C22×Q8×C137—21no—
65C23×C4×C137—21no—
66C23×C4×C137C2311yescharacteristic
67C22×C8×C137C2311yescharacteristic
68C22×C8×C137C2311yescharacteristic
69C22×C8×C137C2311yescharacteristic
70C22×C8×C137C2311yescharacteristic
71C4⋊Q8×C137—28no—
72C4⋊Q8×C137—22no—
73C4⋊Q8×C137—22no—
74C4⋊Q8×C137—22no—
75C4⋊Q8×C137D414yes—
76#125×C137—28no—
77#125×C137—22no—
78#125×C137—22no—
79#125×C137—22no—
80#125×C137—22no—
81#125×C137—22no—
82#125×C137D414yes—
83C22⋊Q8×C137—28no—
84C22⋊Q8×C137—28no—
85#117×C137—22no—
86#117×C137—22no—
87#117×C137—22no—
88#117×C137—22no—
89C2×C4⋊C4×C137—21no—
90C2×C4⋊C4×C137—21no—
91C2×C4⋊C4×C137—21no—
92C2×C4⋊C4×C137—21no—
93C2×C4⋊C4×C137—21no—
94C2×C4⋊C4×C137—21no—
95C2×C4⋊C4×C137—21no—
96C2×C4⋊C4×C137—22no—
97C2×C4⋊C4×C137—22no—
98C2×C4⋊C4×C137—21no—
99C2×C4⋊C4×C137—21no—
100C2×C4⋊C4×C137—21no—
101C2×C4⋊C4×C137—21no—
102C2×C4⋊C4×C137—21no—
103C2×C4⋊C4×C137—21no—
104C2×C4⋊C4×C137D411yescharacteristic
105C2×C4⋊C4×C137D411yescharacteristic
106C2×C4⋊C4×C137C2311yescharacteristic
107C2×C4⋊C4×C137C2311yescharacteristic
108C2×C4⋊C4×C137C2311yescharacteristic
109C2×C4⋊C4×C137C2311yescharacteristic
110C2×C4⋊C4×C137C2311yescharacteristic
111C2×C4⋊C4×C137C2311yescharacteristic
112C2×C4⋊C4×C137C2311yescharacteristic
113C2×C4⋊C4×C137C2311yescharacteristic
114C2×C22⋊C4×C137—21no—
115C2×C22⋊C4×C137—21no—
116C2×C22⋊C4×C137—21no—
117C2×C22⋊C4×C137D411yescharacteristic
118C2×C22⋊C4×C137D411yescharacteristic
119C2×C42×C137—21no—
120C2×C42×C137C2311yescharacteristic
121C2×C42×C137C2311yescharacteristic
122#107×C137—22no—
123#107×C137—22no—
124#107×C137—22no—
125#107×C137—22no—
126#106×C137—22no—
127#106×C137—22no—
128#106×C137—22no—
129#106×C137—22no—
130C22⋊C8×C137Q814yescomplemented
131C22⋊C8×C137Q814yescomplemented
132#97×C137—22no—
133C4×C8×C137—22no—
134#95×C137—21no—
135#95×C137—21no—
136#95×C137—21no—
137#95×C137—21no—
138C24×C137C2×D411yescharacteristic
139C2×Q8×C137—24no—
140C2×Q8×C137—24no—
141C2×Q8×C137—81no—
142C2×Q8×C137—81no—
143C2×Q8×C137—81no—
144C2×Q8×C137—81no—
145C22×C4×C137—21no—
146C22×C4×C137—21no—
147C22×C4×C137—21no—
148C22×C4×C137—21no—
149C22×C4×C137—21no—
150C22×C4×C137—21no—
151C22×C4×C137—21no—
152C22×C4×C137—21no—
153C22×C4×C137—24no—
154C22×C4×C137—21no—
155C22×C4×C137—21no—
156C22×C4×C137—21no—
157C22×C4×C137—21no—
158C22×C4×C137—81no—
159C22×C4×C137—81no—
160C22×C4×C137C2×D411yescharacteristic
161C22×C4×C137C2×D411yescharacteristic
162C22×C4×C137C2×D411yescharacteristic
163C22×C4×C137C2×D411yescharacteristic
164C22×C4×C137C2×D411yescharacteristic
165C22×C4×C137C2×Q812yes—
166C22×C4×C137C2×Q812yes—
167C22×C4×C137C2411yescharacteristic
168C2×C8×C137—21no—
169C2×C8×C137—21no—
170C2×C8×C137—21no—
171C2×C8×C137—21no—
172C2×C8×C137—21no—
173C2×C8×C137—21no—
174C2×C8×C137—21no—
175C2×C8×C137—21no—
176C2×C8×C137C2×Q812yes—
177C2×C8×C137C2×Q812yes—
178C2×C8×C137C2×Q812yes—
179C2×C8×C137C2×Q812yes—
180C4⋊C4×C137—24no—
181C4⋊C4×C137—24no—
182C4⋊C4×C137—24no—
183C4⋊C4×C137—24no—
184C4⋊C4×C137—24no—
185C4⋊C4×C137—24no—
186C4⋊C4×C137—24no—
187C4⋊C4×C137—22no—
188C4⋊C4×C137—22no—
189C4⋊C4×C137—21no—
190C4⋊C4×C137—21no—
191C4⋊C4×C137—21no—
192C4⋊C4×C137—21no—
193C4⋊C4×C137—21no—
194C4⋊C4×C137—21no—
195C4⋊C4×C137—21no—
196C4⋊C4×C137—21no—
197C4⋊C4×C137—21no—
198C4⋊C4×C137—21no—
199C4⋊C4×C137—21no—
200C4⋊C4×C137—21no—
201C4⋊C4×C137—42no—
202C4⋊C4×C137—42no—
203C4⋊C4×C137—81no—
204C4⋊C4×C137—81no—
205C4⋊C4×C137—81no—
206C4⋊C4×C137—81no—
207C4⋊C4×C137C2×D412yes—
208C4⋊C4×C137C2×D412yes—
209C4⋊C4×C137C2×D412yes—
210C4⋊C4×C137C2×D412yes—
211C22⋊C4×C137—24no—
212C22⋊C4×C137—22no—
213C22⋊C4×C137—22no—
214C22⋊C4×C137—81no—
215C22⋊C4×C137—81no—
216C42×C137—24no—
217C42×C137—21no—
218C42×C137—21no—
219C42×C137C2×D412yes—
220C42×C137C2×D412yes—
221C23×C137—21no—
222C23×C137—21no—
223C23×C137—21no—
224C23×C137—21no—
225C23×C137—21no—
226C23×C137—21no—
227C23×C137C4⋊Q812yes—
228C23×C137C22×D411yescharacteristic
229Q8×C137—84no—
230Q8×C137—84no—
231C2×C4×C137—21no—
232C2×C4×C137—21no—
233C2×C4×C137—21no—
234C2×C4×C137—21no—
235C2×C4×C137—21no—
236C2×C4×C137—21no—
237C2×C4×C137—22no—
238C2×C4×C137—22no—
239C2×C4×C137—22no—
240C2×C4×C137—22no—
241C2×C4×C137—21no—
242C2×C4×C137—22no—
243C2×C4×C137—21no—
244C2×C4×C137—22no—
245C2×C4×C137—22no—
246C2×C4×C137—22no—
247C2×C4×C137—21no—
248C2×C4×C137—21no—
249C2×C4×C137—21no—
250C2×C4×C137—21no—
251C2×C4×C137—41no—
252C2×C4×C137—41no—
253C2×C4×C137—41no—
254C2×C4×C137—41no—
255C2×C4×C137—41no—
256C2×C4×C137—41no—
257C2×C4×C137—41no—
258C2×C4×C137—41no—
259C2×C4×C137—41no—
260C2×C4×C137—41no—
261C2×C4×C137—41no—
262C2×C4×C137—41no—
263C2×C4×C137—41no—
264C2×C4×C137—41no—
265C2×C4×C137—41no—
266C2×C4×C137—41no—
267C2×C4×C137—41no—
268C2×C4×C137—41no—
269C2×C4×C137—41no—
270C2×C4×C137—41no—
271C2×C4×C137—84no—
272C2×C4×C137#12012yes—
273C2×C4×C137#12012yes—
274C2×C4×C137C4⋊Q812yes—
275C2×C4×C137C22×D411yescharacteristic
276C2×C4×C137C22×D411yescharacteristic
277C2×C4×C137C22×Q811yescharacteristic
278C2×C4×C137C22×Q811yescharacteristic
279C2×C4×C1372−1+411yescharacteristic
280C2×C4×C1372−1+411yescharacteristic
281C8×C137—22no—
282C8×C137—22no—
283C8×C137—22no—
284C8×C137—22no—
285C22×C137—22no—
286C22×C137—22no—
287C22×C137—22no—
288C22×C137—41no—
289C22×C137—41no—
290C22×C137—41no—
291C22×C137—41no—
292C22×C137C2×#12011yescharacteristic
293C22×C137C2×C4⋊Q811yescharacteristic
294C22×C137#53611yescharacteristic
295C22×C137#57611yescharacteristic
296C22×C137#57711yescharacteristic
297C22×C137#57711yescharacteristic
298C22×C137#57811yescharacteristic
299C4×C137—22no—
300C4×C137—22no—
301C4×C137—22no—
302C4×C137—41no—
303C4×C137—42no—
304C4×C137—42no—
305C4×C137—42no—
306C4×C137—41no—
307C4×C137—42no—
308C4×C137—81no—
309C4×C137—81no—
310C4×C137—81no—
311C4×C137—81no—
312C4×C137D4×Q811yescharacteristic
313C4×C137D4×Q811yescharacteristic
314C4×C137D4×Q811yescharacteristic
315C4×C137D4×Q811yescharacteristic
316C2×C137—42no—
317C2×C137#243411yescharacteristic
318C2×C137#301211yescharacteristic
319C2×C137#301311yescharacteristic
320C2×C137#316311yescharacteristic
321C2×C137#316411yescharacteristic
322C2×C137#324111yescharacteristic
323C2×C137#324211yescharacteristic
324#25822C13711yesmaximal, characteristic, direct product factor, Sylow
325C137#2582211yescharacteristic, direct product factor, Sylow
326C2×#544C2×C13711yescharacteristic
327C2×#501C2×C13711yescharacteristic, complemented
328C2×#499C2×C13711yescharacteristic, complemented
329#2629C2×C13711yescharacteristic
330#2059C2×C13711yescharacteristic, complemented
331#2059C2×C13711yescharacteristic, complemented
332#2058C2×C13711yescharacteristic, complemented
333#2057C2×C13711yescharacteristic, complemented
334#1992C2×C13711yescharacteristic, complemented
335#1990C2×C13711yescharacteristic, complemented
336#1854C2×C13711yescharacteristic
337#1854C2×C13711yescharacteristic
338#1853C2×C13711yescharacteristic
339#1852C2×C13711yescharacteristic
340#1750C2×C13711yescharacteristic
341#544—24no—
342#544—24no—
343C2×C4⋊Q8—21no—
344C2×C4⋊Q8C22×C13711yescharacteristic
345C2×C4⋊Q8C22×C13711yescharacteristic
346C2×#125—21no—
347C2×#125C22×C13711yescharacteristic
348C2×#125C22×C13711yescharacteristic
349C2×#125C22×C13711yescharacteristic
350C2×C22⋊Q8—21no—
351C2×C22⋊Q8—21no—
352C2×#117C22×C13711yescharacteristic
353C2×#117C22×C13711yescharacteristic
354C22×C4⋊C4C22×C13711yescharacteristic
355#501—24no—
356#499—24no—
357C2×#107C22×C13711yescharacteristic
358C2×#107C22×C13711yescharacteristic
359C2×#107C22×C13711yescharacteristic
360C2×#107C22×C13711yescharacteristic
361C2×#106C22×C13711yescharacteristic
362C2×#106C22×C13711yescharacteristic
363C2×#106C22×C13711yescharacteristic
364C2×#106C22×C13711yescharacteristic
365C2×C22⋊C8C22×C13711yescharacteristic
366C2×C22⋊C8C22×C13711yescharacteristic
367C2×#97C22×C13711yescharacteristic
368C2×C4×C8C22×C13711yescharacteristic
369#398—21no—
370#398—21no—
371#396—21no—
372#396—21no—
373#389C22×C13711yescharacteristic
374#389C22×C13711yescharacteristic
375#384C22×C13711yescharacteristic
376#380C22×C13711yescharacteristic
377#380C22×C13711yescharacteristic
378#340C22×C13711yescharacteristic
379#340C22×C13711yescharacteristic
380#340C22×C13711yescharacteristic
381#340C22×C13711yescharacteristic
382#340C22×C13711yescharacteristic
383#340C22×C13711yescharacteristic
384#340C22×C13711yescharacteristic
385#340C22×C13711yescharacteristic
386#336C22×C13711yescharacteristic
387#336C22×C13711yescharacteristic
388C22×Q8—21no—
389C22×Q8—21no—
390C23×C4—21no—
391C23×C4C23×C13711yescharacteristic
392C22×C8C23×C13711yescharacteristic
393C22×C8C23×C13711yescharacteristic
394C22×C8C23×C13711yescharacteristic
395C22×C8C23×C13711yescharacteristic
396C4⋊Q8—28no—
397C4⋊Q8—22no—
398C4⋊Q8—22no—
399C4⋊Q8—22no—
400C4⋊Q8D4×C13714yes—
401#125—28no—
402#125—22no—
403#125—22no—
404#125—22no—
405#125—22no—
406#125—22no—
407#125D4×C13714yes—
408C22⋊Q8—28no—
409C22⋊Q8—28no—
410#117—22no—
411#117—22no—
412#117—22no—
413#117—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4D4×C13711yescharacteristic
430C2×C4⋊C4D4×C13711yescharacteristic
431C2×C4⋊C4C23×C13711yescharacteristic
432C2×C4⋊C4C23×C13711yescharacteristic
433C2×C4⋊C4C23×C13711yescharacteristic
434C2×C4⋊C4C23×C13711yescharacteristic
435C2×C4⋊C4C23×C13711yescharacteristic
436C2×C4⋊C4C23×C13711yescharacteristic
437C2×C4⋊C4C23×C13711yescharacteristic
438C2×C4⋊C4C23×C13711yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4D4×C13711yescharacteristic
443C2×C22⋊C4D4×C13711yescharacteristic
444C2×C42—21no—
445C2×C42C23×C13711yescharacteristic
446C2×C42C23×C13711yescharacteristic
447#107—22no—
448#107—22no—
449#107—22no—
450#107—22no—
451#106—22no—
452#106—22no—
453#106—22no—
454#106—22no—
455C22⋊C8Q8×C13714yescomplemented
456C22⋊C8Q8×C13714yescomplemented
457#97—22no—
458C4×C8—22no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463C24C2×D4×C13711yescharacteristic
464C2×Q8—24no—
465C2×Q8—24no—
466C2×Q8—81no—
467C2×Q8—81no—
468C2×Q8—81no—
469C2×Q8—81no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4C2×D4×C13711yescharacteristic
486C22×C4C2×D4×C13711yescharacteristic
487C22×C4C2×D4×C13711yescharacteristic
488C22×C4C2×D4×C13711yescharacteristic
489C22×C4C2×D4×C13711yescharacteristic
490C22×C4C2×Q8×C13712yes—
491C22×C4C2×Q8×C13712yes—
492C22×C4C24×C13711yescharacteristic
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8C2×Q8×C13712yes—
502C2×C8C2×Q8×C13712yes—
503C2×C8C2×Q8×C13712yes—
504C2×C8C2×Q8×C13712yes—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—81no—
529C4⋊C4—81no—
530C4⋊C4—81no—
531C4⋊C4—81no—
532C4⋊C4C2×D4×C13712yes—
533C4⋊C4C2×D4×C13712yes—
534C4⋊C4C2×D4×C13712yes—
535C4⋊C4C2×D4×C13712yes—
536C22⋊C4—24no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—81no—
540C22⋊C4—81no—
541C42—24no—
542C42—21no—
543C42—21no—
544C42C2×D4×C13712yes—
545C42C2×D4×C13712yes—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23C4⋊Q8×C13712yes—
553C23C22×D4×C13711yescharacteristic
554Q8—84no—
555Q8—84no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—84no—
597C2×C4#120×C13712yes—
598C2×C4#120×C13712yes—
599C2×C4C4⋊Q8×C13712yes—
600C2×C4C22×D4×C13711yescharacteristic
601C2×C4C22×D4×C13711yescharacteristic
602C2×C4C22×Q8×C13711yescharacteristic
603C2×C4C22×Q8×C13711yescharacteristic
604C2×C42−1+4×C13711yescharacteristic
605C2×C42−1+4×C13711yescharacteristic
606C8—22no—
607C8—22no—
608C8—22no—
609C8—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22C2×#120×C13711yescharacteristic
618C22C2×C4⋊Q8×C13711yescharacteristic
619C22#536×C13711yescharacteristic
620C22#576×C13711yescharacteristic
621C22#577×C13711yescharacteristic
622C22#577×C13711yescharacteristic
623C22#578×C13711yescharacteristic
624C4—22no—
625C4—22no—
626C4—22no—
627C4—41no—
628C4—42no—
629C4—42no—
630C4—42no—
631C4—41no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—81no—
637C4D4×Q8×C13711yescharacteristic
638C4D4×Q8×C13711yescharacteristic
639C4D4×Q8×C13711yescharacteristic
640C4D4×Q8×C13711yescharacteristic
641C2—42no—
642C2#2434×C13711yescharacteristic
643C2#3012×C13711yescharacteristic
644C2#3013×C13711yescharacteristic
645C2#3163×C13711yescharacteristic
646C2#3164×C13711yescharacteristic
647C2#3241×C13711yescharacteristic
648C2#3242×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC24×C137C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×#117×C137 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#501×C137C2semidirect
3. C2×#499×C137C2semidirect
5. #2059×C137C2semidirect
6. #2059×C137C2semidirect
7. #2058×C137C2semidirect
8. #2057×C137C2semidirect
9. #1992×C137C2semidirect
10. #1990×C137C2semidirect
130. C22⋊C8×C137Q8semidirect
131. C22⋊C8×C137Q8semidirect
324. #25822C137direct (N × H)
325. C137#25822direct (N × H)
327. C2×#501C2×C137semidirect
328. C2×#499C2×C137semidirect
330. #2059C2×C137semidirect
331. #2059C2×C137semidirect
332. #2058C2×C137semidirect
333. #2057C2×C137semidirect
334. #1992C2×C137semidirect
335. #1990C2×C137semidirect
455. C22⋊C8Q8×C137semidirect
456. C22⋊C8Q8×C137semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#544×C1372
C2×#501×C1372
C2×#499×C1372
#2629×C1372
#2059×C1372
#2058×C1372
#2057×C1372
#1992×C1372
#1990×C1372
#1854×C1372
#1853×C1372
#1852×C1372
#1750×C1372
#25822137